# To index or not to index?

Figure 1: (Upper) The historical North Atlantic Oscillation (NAO) index calculated as the difference between the Icelandic Low (L) and the Azores High (H) during the winter season (December – March) (from Martin Visbeck). (Lower) The pattern associated with a positive (NAO+; right) and a negative (NAO-; left) phase of the index. NAO+ indicates a larger pressure difference between the centers of H and L, resulting in stronger westerly winds which brings along more rain and milder temperatures from North America, over the North Atlantic Ocean and towards Northern Europe. During NAO- both L and H, and hence the westerly winds are weaker and more zonal, which brings the storms more into central Europe, leaving northern Europe cold and dry (Thomson Higher Education).

Imagine trying to explain whether or not it is a wet and warm winter on the western coast of Norway based on the surface air pressure in Iceland. Sounds far fetched? That’s in a way what researchers do to simplify the complexity of the atmosphere to something that we can easily handle and understand. This simplification is an index. I will illustrate that indices can be a good approach to simplifying science, but we need to know the limitations. Problems arise when we think we know what an index means, but we don’t.

An index is a simplification of a 2D pattern (map or cross-section) representing for example a certain weather situation, oceanic currents, physical process etc. This simplification leaves us with one number to represent a large-scale situation at one specific point in time. We can then look at how the index itself varies in time, and how the large-scale spatial pattern varies in relation to the index. This approach is used both for oceanic and atmospheric circulation, sea surface temperature variations and several other variables.

Indices can in general be used in two ways. Firstly, we can use a measurement or a number to represent a larger area of the same variable. For example sea level pressure in one place can represent a larger area surrounding that spot. This measurement can also vary synchronously with other areas, but in the opposite direction (if the air pressure drops at one place, it has to increase somewhere else). In this way we can map the pattern of how all the values vary in relation to our original measurement. Secondly, we can use the relationship between what we have measured and other variables. For example, when a storm is approaching (low pressure) we also assume that this storm will be followed by rain and, in winter, also relatively warm temperatures.

One very popular index is the North Atlantic Oscillation (NAO) index (see Figure 1). It explains what is going on in the atmosphere over the North Atlantic and Arctic. There are several different ways of calculating this index, but they all say something about the strength of the westerly winds crossing the North Atlantic from the coast of the US towards Europe. The index can also give indications of how stormy northern Europe will be. One way of defining the index is by taking the difference between the low-pressure system normally situated over Iceland and the high-pressure system normally situated over the Azores. We can calculate the NAO index either by tracking the centers of these pressure systems or by using fixed locations, in addition to several other statistical approaches.

Figure 2: Reconstructions of the slow varying part of the NAO index from various places and climatic records. The black line shows the observations. From Pinto and Raible (2012).

We have available direct observations of sea level pressure from the 1860’s and onwards.These provide us with the information needed to compute the NAO index. The question is whether the relationship between Iceland and the Azores has always existed or if it has changed with time. Several people have tried to reconstruct the NAO index back in time based on the present relationship between the pressure on Iceland and temperature and precipitation at various locations (Figure 2). Although the reconstructions seem to work for the near past (the lines coincide), the further back we go, the more the lines start to diverge. Does this tell us that different processes controlled the temperature and precipitation in the past? Maybe the relationship we see today doesn’t tell us the full story.

The NAO index may still explain much of the variations in storminess over Europe, but we might still run into problems. The strength of the low-pressure system over Iceland is not the only thing that varies. The low-pressure system itself might wander around. How can we capture the resulting temperature and precipitation from a nomadic pressure system?

So what have we learned from this? The conclusion is that an index is a nice and simple approach, and it can produce consistent results as long as you know the limitations. It would be great if the relationship between two variables always holds, but it doesn’t. When it doesn’t it might be masked by something else, or the relationship we have assumed between the two variables might collapse entirely in periods. Nature isn’t always easy to understand, so there are always limitations to every simplification. But at the same time, that’s what makes my job exciting!

References: Pinto, J.G., and C.C. Raible (2012): Past and recent challenges in the North Atlantic Oscillation. Climate Change, 3: 79-90, doi: 10.1002/wcc.150

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#### Iselin Medhaug

I am a PostDoc in climate physics at ETH Zurich. My main research interests are climate variability and mechanisms for variability in the North Atlantic ocean, with focus on ocean circulation and heat transport from the tropics to the pole on time scales from years to decades. Another aspect of my research concerns natural variations versus human induced effects on climate including the recent halt in the increase of global warming.

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